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- W2964797420 abstract "We give offline algorithms for processing a sequence of 2- and 3-edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for 3-edge and 3-vertex connectivity require (O(n^{2/3})) and O(n) time per update, respectively, our per-operation cost is only (O(log n)), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, including online models." @default.
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- W2964797420 date "2019-01-01" @default.
- W2964797420 modified "2023-10-18" @default.
- W2964797420 title "Optimal Offline Dynamic 2, 3-Edge/Vertex Connectivity" @default.
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- W2964797420 doi "https://doi.org/10.1007/978-3-030-24766-9_40" @default.
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